Measuring the Reduced Shear

Neglecting the second order corrections in weak lensing measurements can lead to a few percent uncertainties on cosmic shears, and becomes more important for cluster lensing mass reconstructions. Existing methods which claim to measure the reduced shears are not necessarily accurate to the second order when a point spread function (PSF) is present. We show that the method of Zhang (2008) exactly measures the reduced shears at the second order level in the presence of PSF. A simple theorem is provided for further confirming our calculation, and for judging the accuracy of any shear measurement method at the second order based on its properties at the first order. The method of Zhang (2008) is well defined mathematically. It does not require assumptions on the morphologies of galaxies and the PSF. To reach a sub-percent level accuracy, the CCD pixel size is required to be not larger than 1/3 of the Full Width at Half Maximum (FWHM) of the PSF. Using a large ensemble (> 10^7) of mock galaxies of unrestricted morphologies, we find that contaminations to the shear signals from the noise of background photons can be removed in a well defined way because they are not correlated with the source shapes. The residual shear measurement errors due to background noise are consistent with zero at the sub-percent level even when the amplitude of such noise reaches about 1/10 of the source flux within the half-light radius of the source. This limit can in principle be extended further with a larger galaxy ensemble in our simulations. On the other hand, the source Poisson noise remains to be a cause of systematic errors. For a sub-percent level accuracy, our method requires the amplitude of the source Poisson noise to be less than 1/80 ~ 1/100 of the source flux within the half-light radius of the source, corresponding to collecting roughly 10^4 source photons.Comment: 18 pages, 3 figures, 4 tables, minor changes from the previous versio

A low-voltage retarding-field Mott polarimeter for photocathode characterization

Nuclear physics experiments at Thomas Jefferson National Accelerator Facility's CEBAF rely on high polarization electron beams. We describe a recently commissioned system for prequalifying and studying photocathodes for CEBAF with a load-locked, low-voltage polarized electron source coupled to a compact retarding-field Mott polarimeter. The polarimeter uses simplified electrode structures and operates from 5 to 30 kV. The effective Sherman function for this device has been calibrated by comparison with the CEBAF 5 MeV Mott polarimeter. For elastic scattering from a thick gold target at 20 keV, the effective Sherman function is 0.201(5). Its maximum efficiency at 20 keV, defined as the detected count rate divided by the incident particle current, is 5.4(2) x 10-4, yielding a figure-of-merit, or analyzing power squared times efficiency, of 1.0(1) x 10-5. The operating parameters of this new polarimeter design are compared to previously published data for other compact Mott polarimeters of the retarding-field type.Comment: 9 figure

Chemical telemetry of OH observed to measure interstellar magnetic fields

We present models for the chemistry in gas moving towards the ionization front of an HII region. When it is far from the ionization front, the gas is highly depleted of elements more massive than helium. However, as it approaches the ionization front, ices are destroyed and species formed on the grain surfaces are injected into the gas phase. Photodissociation removes gas phase molecular species as the gas flows towards the ionization front. We identify models for which the OH column densities are comparable to those measured in observations undertaken to study the magnetic fields in star forming regions and give results for the column densities of other species that should be abundant if the observed OH arises through a combination of the liberation of H2O from surfaces and photodissociation. They include CH3OH, H2CO, and H2S. Observations of these other species may help establish the nature of the OH spatial distribution in the clouds, which is important for the interpretation of the magnetic field results.Comment: 11 pages, 2 figures, accepted by Astrophysics and Space Scienc

Topological mirror symmetry with fluxes

Motivated by SU(3) structure compactifications, we show explicitly how to construct half--flat topological mirrors to Calabi--Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential--geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi--Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza--Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.Comment: 35 pages, 5 figure

Neutron scattering and molecular correlations in a supercooled liquid

We show that the intermediate scattering function $S_n(q,t)$ for neutron scattering (ns) can be expanded naturely with respect to a set of molecular correlation functions that give a complete description of the translational and orientational two-point correlations in the liquid. The general properties of this expansion are discussed with special focus on the $q$-dependence and hints for a (partial) determination of the molecular correlation functions from neutron scattering results are given. The resulting representation of the static structure factor $S_n(q)$ is studied in detail for a model system using data from a molecular dynamics simulation of a supercooled liquid of rigid diatomic molecules. The comparison between the exact result for $S_n(q)$ and different approximations that result from a truncation of the series representation demonstrates its good convergence for the given model system. On the other hand it shows explicitly that the coupling between translational (TDOF) and orientational degrees of freedom (ODOF) of each molecule and rotational motion of different molecules can not be neglected in the supercooled regime.Further we report the existence of a prepeak in the ns-static structure factor of the examined fragile glassformer, demonstrating that prepeaks can occur even in the most simple molecular liquids. Besides examining the dependence of the prepeak on the scattering length and the temperature we use the expansion of $S_n(q)$ into molecular correlation functions to point out intermediate range orientational order as its principle origin.Comment: 13 pages, 7 figure

Synchronization in a System of Globally Coupled Oscillators with Time Delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results

Synchronization and resonance in a driven system of coupled oscillators

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective synchronization of the system, is derived; it is found that the total order parameter decreases monotonically with noise, indicating overall suppression of synchronization. Still, for large coupling strengths, there exists an optimal noise level at which the periodic (ac) component of the order parameter reaches its maximum. The response of the phase velocity is also examined and found to display resonance behavior.Comment: 17 pages, 3 figure

Phase synchronization and noise-induced resonance in systems of coupled oscillators

We study synchronization and noise-induced resonance phenomena in systems of globally coupled oscillators, each possessing finite inertia. The behavior of the order parameter, which measures collective synchronization of the system, is investigated as the noise level and the coupling strength are varied, and hysteretic behavior is manifested. The power spectrum of the phase velocity is also examined and the quality factor as well as the response function is obtained to reveal noise-induced resonance behavior.Comment: to be published in Phys. Rev.

The PL calibration for Milky Way Cepheids and its implications for the distance scale

The rationale behind recent calibrations of the Cepheid PL relation using the Wesenheit formulation is reviewed and reanalyzed, and it is shown that recent conclusions regarding a possible change in slope of the PL relation for short-period and long-period Cepheids are tied to a pathological distribution of HST calibrators within the instability strip. A recalibration of the period-luminosity relation is obtained using Galactic Cepheids in open clusters and groups, the resulting relationship, described by log L/L_sun = 2.415(+-0.035) + 1.148(+-0.044)log P, exhibiting only the moderate scatter expected from color spread within the instability strip. The relationship is confirmed by Cepheids with HST parallaxes, although without the need for Lutz-Kelker corrections, and in general by Cepheids with revised Hipparcos parallaxes, albeit with concerns about the cited precisions of the latter. A Wesenheit formulation of Wv = -2.259(+-0.083) - 4.185(+-0.103)log P for Galactic Cepheids is tested successfully using Cepheids in the inner regions of the galaxy NGC 4258, confirming the independent geometrical distance established for the galaxy from OH masers. Differences between the extinction properties of interstellar and extragalactic dust may yet play an important role in the further calibration of the Cepheid PL relation and its application to the extragalactic distance scale.Comment: Accepted for Publication (Astrophysics & Space Science